CBSE Class 10 · Boards 2027 · NCERT 2026-27 syllabus
NCERT Solutions Class 10 Maths Chapter 1 Real Numbers
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Boards begin February 2027
Pre-boards are in December
Real Numbers is in Number Systems, which carries 6 of the 80 marks in the 2026-27 CBSE Maths paper
There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?
Step 1They both meet at the start when each has completed an integer number of rounds — i.e. after a time that is a multiple of both 18 and 12.
Step-by-step solution
They both meet at the start when each has completed an integer number of rounds — i.e. after a time that is a multiple of both 18 and 12.
The smallest such time is LCM(18, 12).
Prime factorisations: 18 = 2 × 3²; 12 = 2² × 3.
LCM = 2² × 3² = 4 × 9 = 36.
Hence they meet at the starting point after 36 minutes.
CBSE board pattern: Assertion-Reason and case-based questions
Written in the CBSE board format. These are not numbered NCERT/Exemplar questions; some case studies are built on textbook problems. Neither NCERT book has Assertion-Reason questions: they, and case-based questions, are a CBSE board-paper format, here on this chapter's 2026-27 syllabus, with solutions by LazyTopper.
CBSE board pattern · Case-based4 marks
A sweet seller has 420 kaju barfis and 130 badam barfis. She wants to stack them in such a way that each stack has the same number, and they take up the least area of the tray.
(i) What number of barfis should be placed in each stack?
(ii) How many stacks of kaju barfis and how many stacks of badam barfis will be formed?
Step 1To minimise tray area, make each stack as TALL as possible while keeping a uniform stack size that divides both 420 and 130 evenly.
Step-by-step solution
To minimise tray area, make each stack as TALL as possible while keeping a uniform stack size that divides both 420 and 130 evenly.
Largest such number is HCF(420, 130). Factorise: 420 = 2² × 3 × 5 × 7, 130 = 2 × 5 × 13.
HCF = product of smallest powers of common primes = 2 × 5 = 10.
So each stack contains 10 barfis. Kaju stacks = 420/10 = 42. Badam stacks = 130/10 = 13.
Total stacks on the tray = 42 + 13 = 55, each of height 10.
Answer:(i) 10 barfis per stack; (ii) 42 kaju stacks and 13 badam stacks.
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Questions from the NCERT Class 10 Mathematics textbook (the CBSE board-pattern section is in the board format, not numbered book questions); the solutions are written by LazyTopper. LazyTopper is an independent platform and is not affiliated with CBSE or NCERT.